The thinking of the president and administration officials, according to a knowledgeable source, is that while the administration is not explicitly supporting the removal of Morsy from power -- it expressly did not support the move -- it is seeking to push the Egyptian military in a direction.

If the Obama administration were to use the word "coup," it would have legal ramifications that would result in the end of U.S. aid. If White House officials pulled the plug completely, they would be removing themselves from the picture altogether.

Egyptian general: This isn't a coup

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What comes next in Egypt?

The priority for the Obama administration is to preserve some space while trying to contain a fluid and combustible situation, the source said.

The message being conveyed publicly and privately is that Obama accepts that this happened and even sees the potential that it could turn out for the best, given Morsy's autocratic rule.

That said, the president is concerned that the military leaders and the acting leader might see the events as an opening to take on Morsy and the Muslim Brotherhood through excessive force.

Obama's words are intended to put the onus on the military to show restraint and to uphold its pledge to hold parliamentary and presidential elections, the source said.

Notably, the president said he and his officials "are deeply concerned by the decision of the Egyptian armed forces to remove President Morsy and suspend the Egyptian constitution" without suggesting that there would necessarily be any negative repercussions.

Potential repercussions are alluded to in Obama's statement, but never definitively threatened. The president said he had "directed the relevant departments and agencies to review the implications under U.S. law for our assistance to the government of Egypt."

Would the president suspend the $1.5 billion in annual assistance given to the Egyptian government? He never says.

The source says the message is that U.S. action can escalate from reviewing to cutting off if need be, but that the Obama administration is prepared to continue to work with Egyptian military officials if they take this in the right direction.

Refraining from the arbitrary arrests of Muslim Brotherhood members and its supporters would be part of that "right direction," the source said.

For all intents and purposes, this means that as far as the Obama administration is concerned, Morsy is out of luck, and the ball is in the court of Army Chief Gen. Abdel-Fatah El-Sisi.